Nondimensionalization

Get inspired:

This lesson is about making your life easier. Would you rather study the equation

    \[ mr\ddot{\phi} = -b\dot{\phi} - mg\sin \phi + m r \omega^2 \sin \phi \cos \phi \]

which is second order and has five parameters, or the equation

    \[ \phi_\tau =  - \sin \phi + \gamma \sin \phi \cos \phi \]

which is first order and has one parameter? These equations both describe the same system (a particular mechanical system). However, the second one has been put into dimensionless form. Once in dimensionless form, one term has been eliminated because one can make the judgment that that term is small. This is the power of nondimensionaliztion. It can drastically reduce the amount of work you need to do to study a differential equation.

By the end of this lesson, you should be able to:

  • Nondimensionalize differential equations to reduce the number of parameters.

Before class, please:

In class, we will:

After class, please:

  • Do post-class problems.